Re: conundrum regarding propagation of virtual particles
From: Frank Hellmann (Certhas_at_gmail.com)
Date: 10/24/04
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Date: Sun, 24 Oct 2004 14:04:22 +0000 (UTC)
vnemitz@pinn.net (vernonner3voltazim) wrote in message news:<42336979.0410210804.3dca9e1a@posting.google.com>...
> Which brings me to ask whether or not there is
> SOME OTHER technique that works just fine to
> explain QED without sum-over-histories,
Uhmm.... Pick up a QFT course/book. You are mistaking the paths in the
integral for virtual particles. The paths in the integral are all of
real particles which always travel at finite speeds in the end,
virtual particles only appear in the perturbative expansion of the
integral. You can also always do the original operator based QFT.
Furthermore, Feynman path integrals do work for the strong coupling.
The long range behaviour of the strong force comes out right in the
scaling. This is precisely what Gross, Politzer and Wilczek just got
their Nobel prize for.
Of course you can also use cannonical, operator based quantization,
but apparently it's very difficult to make work for the strong
interaction due to gauge invariance. For pathintegrals you use the
Faddeev Popov Ghosts to do this, You need to factor out a vast space
of possible paths related by gauge symmetry and therefore physically
equivalent, there is some highly nontrivial dependency of the space to
mod out on the actual physics in QCD (as opposed to QED which is why
Feynman could get away without it), so what you do is to write the
factors appearing in the path integral as fake physics interacting
with the real physics: Ghost fields.
Basically you have to remember that the more unphysical a path the
less does it contribute to the (quantum) physics. And even though
virtual photons can travell at high speeds, real ones never can.
Furthermore virtual photons only appear in the perturbative expansion
of QED. The perturbative expansion of QCD, however only applies by
virtue of being perturbative, at very high energies (and very short
distances) when the quarks are quasi free and the coupling is weak.
--- frank
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